Linear correlations, asymmetric amplification

Tanaka reported the synthesis of (/ )-muscone (10) by an enantioselective conjugate addition of chiral alkoxydimethylcuprate, which was prepared from chiral ercdo-3-[(l-methylpyrrol-2-yl)methylamino]-l,7,7-trimethylbicyclo[2.2.1]heptan-2-ol (9), methyllithium, and copper iodide (Scheme 9.7) [16]. In this reaction, convex deviation from a linear correlation was observed when the chiral ligand had a higher enantiopurity. This positive NLE was probably induced by the formation of a reactive homochiral dinuclear copper complex to give (R)-muscone. Rossitter also observed asymmetric amplification in a copper-catalyzed conjugate addition of methyl-... 

The value y2 is much higher than the normal value obtained in the linear correlation, hence the term (+)-NLE. Oguni et al. introduced in 1988 the expression asymmetric amplification as being synonymous with (+)-NLE in order to describe these effects. Although this expression is now widely used in the context of nonlinear effects, its validity is questionable (vide supra). 

It was established for several examples that it was possible to observe some departure from the expected proportionality between the enantiomeric excess of the catalyst and the enantiomeric excess of the product. Nonlinear effects (NLE) are categorized as a positive nonlinear effect ((-i-)-NLE) if the curve ee(product) = f(ee(catalyst)) is above the straight line characterizing the expected proportionality between ee(product) and ee(catalyst). The (-i-)-NLE has also been named asymmetric amplification [92]. A negative nonlinear effect ((-)-NLE) means that the experimental curve ee(product) =f( ee(catalyst)) lies below the straight line of the linear correlation. The departure from linearity reflects the formation of diastereomeric species (catalytically active or not) which perturb the predictions based only on mixture of enantiomeric catalysts and the... 

Mikami and coworkers conducted the Diels-Alder reaction with a catalyst prepared by mixing enantiomerically pure R)-56 and racemic 56 and observed a positive nonlinear effect however, they found no asymmetric amplification when they prepared the catalyst by mixing enantiomerically pure R)-56 and enantiomerically pure (S)-56 (i.e., linear correlation between catalyst and product ee). Introduction of molecular sieves restores the asymmetric amplification in the latter case, apparently by equilibration of R) R) and (S)(S) dimers into catalytically less active R) S) dimers. As expected, the reaction rate was faster for R)-56 than for ( )-56 derived from racemic binaphthol hgand ca. 5-fold faster). 

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